ReactJS: How to rerender component after fetching data

So I have a component which displays some data fetched from an external API and saved to localStorage. I have put a fetchData() function that does the job, and I call this function from within componentWillMount(). It looks like this:

The idea here is to check on every render if the data is set in localStorage, otherwise fetch it, save data and then rerender. However, I can't get it to rerender after the data is stored in localStorage. I have tried using